Behind stop lens

ABSTRACT

A behind stop lens has, in succession from the object side, a first lens which is a positive meniscus lens having its convex surface facing the object side, a second lens which is a biconcave negative lens, a third lens which is a biconvex positive lens, and a fourth lens which is a negative meniscus lens having its convex surface facing the image side, the third lens and the fourth lens being cemented together to form a positive cemented lens. The behind stop lens satisfies the following conditions: ##EQU1## where f represents the total focal length of the entire system, Σd represents the distance from the vertex of the object side lens surface of the first lens to the vertex of the image side lens surface of the fourth lens, f 2  represents the focal length of the second lens, r represents the radius of curvature of each lens surface, n and ν represent the refractive index and the Abbe number, respectively, of each lens, and the subscript numbers mean the order from the object side.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to improvements in a modified Tessar type behindstop lens used in a compact camera or the like and having an angle ofview of 60° or more and brightness of the order of F3.5.

2. Description of the Prior Art

As a behind stop lens used in a compact camera and having an angle ofview of 60° or more and brightness of the order of F3.5, there is knowna Tessar type lens and a modified Tessar type lens in which thedirection of the cemented surface of a cemented lens which is a thirdgroup has been changed. Since, however, the stop is positionedrearwardly of the lens, the principal light ray of the oblique lightflux passing through the center of the stop passes through a positionvery far from the optical axis in the neighborhood of the first lensgroup which is most adjacent to the object side, and this leads to astructure in which various aberrations are liable to occur. Due, due tothe fact that the lower light flux relative to the principal light rayof the oblique light flux passes through a point relatively near thecenter of the stop, it performs an especially important role in theimaging performance of the photographic lens. Nevertheless, the lowerlight flux relative to the principal light ray passes through themarginal portion of the forward lens and therefore, substantial coma,chromatic aberration of coma and astigmatism have occurred, and it hasbeen difficult to reduce these aberrations sufficiently at the sametime.

SUMMARY OF THE INVENTION

It is an object of the present invention to overcome the above-noteddisadvantage and to provide a behind stop lens having an angle of viewof 60° or more and brightness of the order of F3.5 in which a reductionin the aberrations of the lower light flux relative to the principallight ray of the oblique light flux is achieved and yet good aberrationbalance as a whole is maintained.

The invention will become fully apparent from the following detaileddescription thereof taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the construction of the lens of the present invention.

FIGS. 2 to 5 show the various aberrations in first to fourth embodimentsof the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The behind stop lens according to the present invention, as shown inFIG. 1, has, in succession from the object side, a first lens L₁ whichis a positive meniscus lens having its convex surface facing the objectside, a second lens L₂ which is a biconcave negative lens, a third lensL₃ which is a biconvex positive lens, and a fourth lens L₄ which is anegative meniscus lens having its convex surface facing the image side,the third lens and the fourth lens being cemented together to form apositive cemented lens, and this behind stop lens satisfies thefollowing conditions: ##EQU2## where f represents the total focal lengthof the entire system, Σd represents the distance from the vertex of theobject side lens surface of the first lens to the vertex of the imageside lens surface of the fourth lens, f₂ represents the focal length ofthe second lens, r represents the radius of curvature of each lenssurface, n and ν represent the refractive index and the Abbe number,respectively, of each lens, and the subscript numbers mean the orderfrom the object side.

In FIG. 1, the states of the light flux from an infinity on-axis objectpoint and the light flux from an infinity off-axis object point having amaximum angle of view are shown to help in understanding the presentinvention.

The conditions of the present invention will hereinafter be described indetail. Condition (1) prescribes the center thickness of the entire lenssystem, and it is a condition for sufficiently securing the quantity ofmarginal light and correcting coma well. That is, in the behind stoplens, the quantity of marginal light is determined by the aperture ofthe lens which is most adjacent to the object side and to make theaperture of the foremost lens small to some degree, it is necessary tosufficiently secure the quantity of marginal light by making thethickness of the entire lens small. In the present invention, ifcondition (1) is departed from, the quantity of light of the light fluxof the oblique light flux which is below the principal light ray will bedeficient and further, the oblique light flux will pass through thefirst lens L₁ at a position far from the optical axis and therefore, thecoma occurring thereat will be great and it will be difficult to effectgood correction even if the burden of correction in the subsequent lenssurfaces is increased.

Condition (2) is a condition for well correcting coma, particularly thecoma of the light rays of the oblique light flux which pass below theprincipal light ray. Generally, in a Tessar type lens, the influence ofthe negative second lens thereof acts intensely so that the light raysbelow the principal light ray, particularly, the light rays in themarginal portion are liable to become divergent and remain as coma.Therefore, by using a positive lens as the third lens, cementing it tothe fourth lens as a negative lens, making the refractive index of thepositive lens which is the third lens moderately high as compared withthe refractive index of the negative lens which is the fourth lens,making the radius of curvature r₆ of the cemented surface convex towardthe image side which is formed by these lenses into a moderate value,and endowing this surface with an intense converging action, theresidual aberration attributable to the aforementioned divergent obliquelight flux can be well corrected with respect to the light flux belowthe principal light ray. If the lower limit of condition (2) isexceeded, the difference in refractive index will become too small andthe converging action by the cemented surface r₆ will becomeinsufficient, so that the occurrence of coma peculiar to the Tessar typelens will become substantial as mentioned above and correction thereofwill be difficult. Conversely, if the upper limit of condition (2) isexceeded, the converging action by the cemented surface r₆ will work toointensely and it will be impossible to correct coma with good balance.

Making the radius of curvature r₆ of the cemented surface of the thirdlens L₃ and the fourth lens L₄ small results in more intenselyconverging the light rays passing below the principal light ray of anoblique light flux, particularly the light rays passing through themarginal portion of the lens, and contributes to better correcting coma.If the lower limit of condition (3) is exceeded, the radius of curvatureof the cemented surface r₆ will become greater and therefore, asdescribed above, the converging action in the marginal portion of thelens will become smaller and better correction of coma will not beaccomplished. However, if the upper limit of condition (3) is exceeded,the radius of curvature of the cemented surface r₆ will become smallerand therefore, the converging action in the marginal portion of the lenswill become excessively great and coma will be aggravated and may not becorrected. Condition (4) is a condition for well correcting particularlythe coma with respect to the upper light flux relative to the principallight ray. The object side surface of the third lens L₃ (the fifthsurface) has the function of converging light rays by having the convexsurface facing the object side, but due to the fact that the angle ofincidence at which the upper light ray relative to the principal lightray is incident on the fifth surface is sharper than the angle ofincidence at which the lower light ray is incident on the fifth surface,the function of converging the upper light ray relative to the principallight ray is more intense. Accordingly, by keeping the radius ofcurvature r₅ of the object side surface of the third lens L₃ at asuitable value, it is possible to well correct coma, particularly, thecoma of the upper light flux relative to the principal light ray. If theupper limit of condition (4) is exceeded, the radius of curvature r₅will become great, whereby the converging action in the fifth surfacewill become too weak. If the lower limit of condition (4) is exceeded,the radius of curvature r₅ will become small, whereby the convergingaction in the fifth surface will become too intense. In any of thesecases, coma cannot be well corrected.

Condition (5) is a condition for correcting chromatic aberration ofcoma, particularly the chromatic aberration of coma of the oblique lightray incident from below the principal light ray which intensely affectsthe imaging performance in the behind stop lens. Generally, thechromatic aberration of coma in a Tessar type lens is intensely affectedby a flint system negative lens as the second lens L₂. That is, lightrays of short wavelength are subjected to a more intense divergingaction by the second lens than light rays of long wavelength, wherebychromatic aberration of coma occurs. Condition (5) is for correcting thechromatic aberration of coma with respect to the lower light fluxrelative to the principal light ray created in the second lens by moreintense divergence, by being also subjected to an intense convergingaction by the cemented lens. That is, glass of high dispersion is usedfor the positive lens L₃ which is the third lens forming the cementedlens and glass of low dispersion is used for the negative lens L₄ whichis the fourth lens, whereby the light rays on the short wavelength sideare more intensely converged under conditions (2) and (3) to therebycorrect chromatic aberration of coma well. If this condition is notsatisfied, chromatic aberration of coma will remain and may not besufficiently corrected.

Condition (6) is a condition for correcting both chromatic aberration ofcoma and longitudinal chromatic aberration. Reducing the occurrence ofchromatic aberration of coma of the light ray below the principal lightray in an oblique light flux is accomplished by using glass of lowerdispersion for the negative lens L₂ as the second lens to minimize thediverging action of light rays of short wavelength and using glass ofhigher dispersion for the positive lens L₃ as the third lens tointensify the converging action. For this purpose, it is necessary thatcondition (5) be satisfied and at the same time, that the Abbe number ν₃of the positive third lens L₃ not exceed the upper limit of condition(6) and the Abbe number ν₂ of the negative second lens L₂ not exceed thelower limit of condition (6). When ν₃ exceeds the upper limit and whenν₂ exceeds the lower limit, the chromatic aberration of coma of thelight flux below the principal light ray will not be sufficientlycorrected. Lower dispersion of the negative second lens L₂ and higherdispersion of the positive third lens L₃ are more desirable for thecorrection of chromatic aberration of coma, but when ν₂ exceeds theupper limit and the dispersion is low and when ν₃ exceeds the lowerlimit and the dispersion is high, longitudinal chromatic aberration willbe under-corrected and will finally not be corrected. Now, lateralchromatic aberration is intensely affected by the first lens L.sub. 1 inwhich the principal light ray which is an oblique light ray is refractedat a position farthest from the optical axis and the second lens L₂ ofhigh dispersion. In the lens of the present invention, the second lensL₂ has a negative power of high dispersion as shown by condition (6) andtherefore, light rays of short wavelength are caused to diverge moreintensely by the second lens. To keep the lateral chromatic aberrationby such divergence good, it is desirable that the Abbe number ν₁ of thefirst lens L₁ which intensely affects the lateral chromatic aberrationbe 45.0<ν₁ <57.0.

Condition (7) is a condition for correcting spherical aberration. If theradius of curvature r₁ of the object side surface of the first lens L₁exceeds the upper limit of this condition, the converging action in thissurface will become weak and spherical aberration will occur in thepositive sense and will not be corrected. On the other hand, if theradius of curvature r₁ exceeds the lower limit of this condition, theconverging action in the object side surface of the first lens L₁ willbecome too intense and therefore, spherical aberration will becomenegative and good correction thereof will be difficult even by acombination of this lens surface with other lens surface.

Condition (8) is a condition for well correcting astigmatism. The imageplane is under-corrected by the positive first lens L₁ and the positivelens comprising the third and fourth lenses L₃ and L₄ cemented together,but over-corrected curvature of image field is caused to occur by thenegative lens L₂ as the second lens to thereby correct the image planewith good balance as a whole. If the upper limit of condition (8) isexceeded, the refractive power of the negative second lens L₂ willbecome too strong and over-corrected curvature of image field willoccur. On the other hand, if the lower limit of condition (8) isexceeded, the refractive power of the negative second lens L₂ will betoo weak and therefore, curvature of image field will be undercorrected.

To correct Petzval sum well, it is desirable that the condition that n₂<1.69 be satisfied with regard to the refractive index n₂ of thenegative second lens L₂ and the condition that n₁ >1.72 be satisfiedwith regard to the refractive index n₁ of the positive first lens L₁.Outside these conditions, Petzval sum will be excessively great in thepositive sense and this is disadvantageous for good correction.

The numerical data of first to fourth embodiments of the presentinvention will be shown below. In the tables below, r represents theradius of curvature of each lens surface, d represents the centerthickness and the air space of each lens, n and ν represent therefractive index and the Abbe number, respectively, of each lens, andthe subscript numbers mean the order from the object side.

    ______________________________________                                        First Embodiment                                                                       f = 100F 3.5                                                         ______________________________________                                        r.sub.1 = 27.6354                                                                        d.sub.1 = 7.8261                                                                         n.sub.1 = 1.77279                                                                         ν.sub.1 = 49.44 L.sub.1                  r.sub.2 = 72.7567                                                                        d.sub.2 = 2.8116                                                   r.sub.3 = -241.1541                                                                      d.sub.3 = 2.6087                                                                         n.sub.2 = 1.68893                                                                         ν.sub.2 = 31.15 L.sub.2                  r.sub.4 = 25.7172                                                                        d.sub.4 = 3.6232                                                   r.sub.5 = 71.2175                                                                        d.sub.5 = 7.8261                                                                         n.sub.3 = 1.74443                                                                         ν.sub.3 = 49.46 L.sub.3                  r.sub.6 = -23.1983                                                                       d.sub.6 = 2.3188                                                                         n.sub.4 = 1.67025                                                                         ν.sub.4 = 57.58 L.sub.4                  r.sub.7 = -133.1722                                                                    Σd = 27.0145                                                            n.sub.3 - n.sub.4 = 0.07418                                                   ν.sub.4 - ν.sub.3 = 8.12                                                f.sub.2 = -33.6                                                      ______________________________________                                    

    ______________________________________                                        Second Embodiment                                                                      f = 100F 3.5                                                         ______________________________________                                        r.sub.1 = 27.7209                                                                        d.sub.1 = 7.8242                                                                         n.sub.1 = 1.77279                                                                         ν.sub.1 = 49.44 L.sub.1                  r.sub.2 = 71.8523                                                                        d.sub.2 = 2.8979                                                   r.sub.3 = -234.1553                                                                      d.sub.3 = 2.6081                                                                         n.sub.2 = 1.68893                                                                         ν.sub.2 = 31.15 L.sub.2                  r.sub.4 = 25.7370                                                                        d.sub.4 = 3.6223                                                   r.sub.5 = 68.3140                                                                        d.sub.5 = 7.8242                                                                         n.sub.3 = 1.74443                                                                         ν.sub.3 = 49.46 L.sub.3                  r.sub.6 = -26.6718                                                                       d.sub.6 = 2.3183                                                                         n.sub.4 = 1.62041                                                                         ν.sub.4 = 60.35 L.sub.4                  r.sub.7 = -181.0863                                                                    Σd = 27.0950                                                            n.sub.3 - n.sub.4 = 0.12402                                                   ν.sub.4 - ν.sub.3 = 10.89                                               f.sub.2 = -33.5                                                      ______________________________________                                    

    ______________________________________                                        Third Embodiment                                                                       f = 100F 3.5                                                         ______________________________________                                        r.sub.1 = 26.8493                                                                        d.sub.1 = 7.2464                                                                         n.sub.1 = 1.74443                                                                         ν.sub.1 = 49.46 L.sub.1                  r.sub.2 = 69.5130                                                                        d.sub.2 = 2.7536                                                   r.sub.3 = -243.6638                                                                      d.sub.3 = 3.1884                                                                         n.sub.2 = 1.67270                                                                         ν.sub.2 = 32.16 L.sub.2                  r.sub.4 = 25.0290                                                                        d.sub.4 = 3.4783                                                   r.sub.5 = 63.3130                                                                        d.sub.5 = 7.5362                                                                         n.sub.3 = 1.74443                                                                         ν.sub.3 = 49.46 L.sub.3                  r.sub.6 = -27.4261                                                                       d.sub.6 = 2.3188                                                                         n.sub.4 = 1.61025                                                                         ν.sub.4 = 56.66 L.sub.4                  r.sub.7 = -238.5099                                                                    Σd = 26.5217                                                            n.sub.3 - n.sub.4 = 0.13418                                                   ν.sub.4 - ν.sub.3 = 7.20                                                f.sub.2 = -33.6                                                      ______________________________________                                    

    ______________________________________                                        Fourth Embodiment                                                                      f = 100F 3.5                                                         ______________________________________                                        r.sub.1 = 29.0490                                                                        d.sub.1 = 7.2463                                                                         n.sub.1 = 1.77279                                                                         ν.sub.1 = 49.44 L.sub.1                  r.sub.2 = 72.4370                                                                        d.sub.2 = 2.8985                                                   r.sub.3 = -199.3606                                                                      d.sub.3 = 4.5991                                                                         n.sub.2 = 1.68893                                                                         ν.sub.2 = 31.15 L.sub.2                  r.sub.4 = 27.7180                                                                        d.sub.4 = 3.2733                                                   r.sub.5 = 68.1066                                                                        d.sub.5 = 6.3339                                                                         n.sub.3 = 1.77279                                                                         ν.sub.3 = 49.44 L.sub.3                  r.sub.6 = -30.2983                                                                       d.sub.6 = 2.3188                                                                         n.sub.4 = 1.62041                                                                         ν.sub.4 = 60.35 L.sub.4                  r.sub.7 = -208.3312                                                                    Σd = 26.6699                                                            n.sub.3 - n.sub.4 = 0.15238                                                   ν.sub.4 - ν.sub.3 = 10.91                                               f.sub.2 = -35.0                                                      ______________________________________                                    

The various aberrations in the first to fourth embodiments are shown inFIGS. 2 to 5, respectively. Spherical aberration, astigmatism,distortion, lateral chromatic aberration and coma are shown in each ofthe aberration graphs. The standard wavelength is d-line (λ=587.6 nm)and g-line (λ=435.8 nm) is used to represent chromatic aberration.

From the aberration graphs, it is apparent that in each of theembodiments, coma is well corrected and each of the embodiments isexcellent in balance of aberrations.

As described above, according to the present invention, a behind stoplens is achieved which has an angle of view of 60° or more and F-numberof the order of 3.5 and yet has a good aberration balance and anexcellent imaging performance.

I claim:
 1. A behind stop lens having an angle of view of 60 degrees ormore and brightness of the order of F3.5 in which aberrations,especially coma and chromatic aberration, are well corrected including,in succession from the object side, a first lens which is a positivemeniscus lens having its convex surface facing the object side, a secondlens which is a biconcave negative lens, a third lens which is abiconvex positive lens, and a fourth lens which is a negative meniscuslens having its convex surface facing the image side, said third lensand said fourth lens being cemented together to form a positive cementedlens, the dispersion of said third lens being higher than that of saidfourth lens so as to correct coma and chromatic aberration, said behindstop lens satisfying the following conditions: ##EQU3## where frepresents the total focal length of the entire system, Σd representsthe distance from the vertex of the object side lens surface of saidfirst lens to the vertex of the image side lens surface of said fourthlens, f₂ represents the focal length of said second lens, r representsthe radius of curvature of each lens surface, n and ν represents therefractive index and the Abbe number, respectively, of each lens, andthe subscript numbers mean the order from the object side.
 2. A behindstop lens according to claim 1, further satisfying the followingconditions:45.0<ν₁ <57.0 n₁ >1.72 n₂ <1.69where ν₁ is the Abbe number ofsaid first lens, n₁ is the refractive index of said first lens and n₂ isthe refractive index of said second lens.
 3. A behind stop lensaccording to claim 2, wherein numerical data are as follows:

    ______________________________________                                                 f = 100F 3.5                                                         ______________________________________                                        r.sub.1 = 27.6354                                                                        d.sub.1 = 7.8261                                                                         n.sub.1 = 1.77279                                                                         ν.sub.1 = 49.44 L.sub.1                  r.sub.2 = 72.7567                                                                        d.sub.2 = 2.8116                                                   r.sub.3 = -241.1541                                                                      d.sub.3 = 2.6087                                                                         n.sub.2 = 1.68893                                                                         ν.sub.2 = 31.15 L.sub.2                  r.sub.4 = 25.7172                                                                        d.sub.4 = 3.6232                                                   r.sub.5 = 71.2175                                                                        d.sub.5 = 7.8261                                                                         n.sub.3 = 1.74443                                                                         ν.sub.3 = 49.46 L.sub.3                  r.sub.6 = -23.1983                                                                       d.sub.6 = 2.3188                                                                         n.sub.4 = 1.67025                                                                         ν.sub.4 = 57.58 L.sub.4                  r.sub.7 = -133.1722                                                                    Σd = 27.0145                                                            n.sub.3 - n.sub.4 = 0.07418                                                   ν.sub.4 - ν.sub.3 = 8.12                                                f.sub.2 = -33.6                                                      ______________________________________                                    

where r represents the radius of curvature of each lens surface, drepresents the center thickness and the air space of each lens, n and νrepresent the refractive index and the Abbe number, respectively, ofeach lens, and the subscript numbers mean the order from the objectside.
 4. A behind stop lens according to claim 2, wherein numerical dataare as follows:

    ______________________________________                                                 f = 100F 3.5                                                         ______________________________________                                        r.sub.1 = 27.7209                                                                        d.sub.1 = 7.8242                                                                         n.sub.1 = 1.77279                                                                         ν.sub.1 = 49.44 L.sub.1                  r.sub.2 = 71.8523                                                                        d.sub.2 = 2.8969                                                   r.sub.3 = -234.1553                                                                      d.sub.3 = 2.6081                                                                         n.sub.2 = 1.68893                                                                         ν.sub.2 = 31.15 L.sub.2                  r.sub.4 = 25.7370                                                                        d.sub.4 = 3.6223                                                   r.sub.5 = 68.3140                                                                        d.sub.5 = 7.8242                                                                         n.sub.3 = 1.74443                                                                         ν.sub.3 = 49.46 L.sub.3                  r.sub.6 = -26.6718                                                                       d.sub.6 = 2.3183                                                                         n.sub.4 = 1.62041                                                                         ν.sub.4 = 60.35 L.sub.4                  r.sub.7 = -181.0863                                                                    Σd = 27.0950                                                            n.sub.3 - n.sub.4 = 0.12402                                                   ν.sub.4 - ν.sub.3 = 10.89                                               f.sub.2 = -33.5                                                      ______________________________________                                    

where r represents the radius of curvature of each lens surface, drepresents the center thickness and the air space of each lens, n and νrepresent the refractive index and the Abbe number, respectively, ofeach lens, and the subscript numbers means the order from the objectside.
 5. A behind stoplens according to claim 2, wherein numerical dataare as follows:

    ______________________________________                                                 f = 100F 3.5                                                         ______________________________________                                        r.sub.1 = 26.8493                                                                        d.sub.1 = 7.2464                                                                         n.sub.1 = 1.74443                                                                         ν.sub.1 = 49.46 L.sub.1                  r.sub.2 = 69.5130                                                                        d.sub.2 = 2.7536                                                   r.sub.3 = -243.6638                                                                      d.sub.3 = 3.1884                                                                         n.sub.2 = 1.67270                                                                         ν.sub.2 = 32.16 L.sub.2                  r.sub.4 = 25.0290                                                                        d.sub.4 = 3.4783                                                   r.sub.5 = 63.3130                                                                        d.sub.5 = 7.5362                                                                         n.sub.3 = 1.74443                                                                         ν.sub.3 = 49.46 L.sub.3                  r.sub.6 = -27.4261                                                                       d.sub.6 = 2.3188                                                                         n.sub.4 = 1.61025                                                                         ν.sub.4 = 56.66 L.sub.4                  r.sub.7 = -238.5099                                                                    Σd = 26.5217                                                            n.sub.3 - n.sub.4 = 0.13418                                                   ν.sub.4 - ν.sub.3 = 7.20                                                f.sub.2 = -33.6                                                      ______________________________________                                    

where r represents the radius of curvature of each lens surface, drepresents the center thickness and the air space of each lens, n and νrepresents the refractive index and the Abbe number, respectively, ofeach lens, and the subscript numbers mean the order from the objectside.
 6. A behind stop lens according to claim 2, wherein numbericaldata are as follows:

    ______________________________________                                                 f = 100F 3.5                                                         ______________________________________                                        r.sub.1 = 29.0490                                                                        d.sub.1 = 7.2463                                                                         n.sub.1 = 1.77279                                                                         ν.sub.1 = 49.44 L.sub.1                  r.sub.2 = 72.4370                                                                        d.sub.2 = 2.8985                                                   r.sub.3 = -199.3606                                                                      d.sub.3 = 4.5991                                                                         n.sub.2 = 1.68893                                                                         ν.sub.2 = 31.15 L.sub.2                  r.sub.4 = 27.7180                                                                        d.sub.4 = 3.2733                                                   r.sub.5 = 68.1066                                                                        d.sub.5 = 6.3339                                                                         n.sub.3 = 1.77279                                                                         ν.sub.3 = 49.44 L.sub.3                  r.sub.6 = -30.2983                                                                       d.sub.6 = 2.3188                                                                         n.sub.4 = 1.62041                                                                         ν.sub.4 = 60.35 L.sub.4                  r.sub.7 = -208.3312                                                                    Σd = 26.6699                                                            n.sub.3 - n.sub.4 = 0.15238                                                   ν.sub.4 - ν.sub.3 = 10.91                                               f.sub.2 = -35.0                                                      ______________________________________                                    

where r represents the radius of curvature of each lens surface, drepresents the center thickness and the air space of each lens, n and νrepresent the refractive index and the Abbe number, respectively, ofeach lens, and the subsript numbers mean the order from the object side.